Question

Check My Work (2 remaining) The mean cost of domestic airfares in the United States rose to an all-time high of $370 per ticket. Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of $105. Use Table 1 in Appendix B. a. What is the probability that a domestic airfare is $550 or more (to 4 decimals)? b. What is the probability that a domestic airfare is $245 or less (to 4 decimals)? c. What if the probability that a domestic airfare is between $310 and $500 (to 4 decimals)? d. What is the cost for the 4% highest domestic airfares? (rounded to nearest dollar) or - Select your answer - Check My Work (2 remaining)

Answer 1

a)

Here, μ = 370, σ = 105 and x = 550. We need to compute P(X >= 550). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (550 - 370)/105 = 1.71

Therefore,
P(X >= 550) = P(z <= (550 - 370)/105)
= P(z >= 1.71)
= 1 - 0.9564 = 0.0436

b)

Here, μ = 370, σ = 105 and x = 245. We need to compute P(X <= 245). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (245 - 370)/105 = -1.19

Therefore,
P(X <= 245) = P(z <= (245 - 370)/105)
= P(z <= -1.19)
= 0.1170

c)
Here, μ = 370, σ = 105, x1 = 310 and x2 = 500. We need to compute P(310<= X <= 500). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z1 = (310 - 370)/105 = -0.57
z2 = (500 - 370)/105 = 1.24

Therefore, we get
P(310 <= X <= 500) = P((500 - 370)/105) <= z <= (500 - 370)/105)
= P(-0.57 <= z <= 1.24) = P(z <= 1.24) - P(z <= -0.57)
= 0.8925 - 0.2843
= 0.6082

d)
z value at 4% = 1.75

z = (x - mean)/sigma
1.75 = (x - 370)/105
x = 105 *1.75 + 370
x = 554